{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:00.693190Z",
     "start_time": "2025-05-10T03:56:00.612504Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from sklearn.cluster import KMeans, AgglomerativeClustering\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage, fcluster\n",
    "from scipy.spatial.distance import squareform"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据均为模拟生成\n",
    "\n",
    "第 1 类数据为来自 N(0, 1) 的 50 个样本\n",
    "\n",
    "第 2 类数据为来自 N(3, 1) 的 50 个样本"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:00.777432Z",
     "start_time": "2025-05-10T03:56:00.770064Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "      <th>x1</th>\n",
       "      <th>x2</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>0</th>\n",
       "      <td>1.624345</td>\n",
       "      <td>-0.611756</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.528172</td>\n",
       "      <td>-1.072969</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.865408</td>\n",
       "      <td>-2.301539</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.744812</td>\n",
       "      <td>-0.761207</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.319039</td>\n",
       "      <td>-0.249370</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x1        x2  y\n",
       "0  1.624345 -0.611756  0\n",
       "1 -0.528172 -1.072969  0\n",
       "2  0.865408 -2.301539  0\n",
       "3  1.744812 -0.761207  0\n",
       "4  0.319039 -0.249370  0"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 生成第 1 类模拟数据\n",
    "np.random.seed(1)\n",
    "cluster1 = np.random.normal(0, 1, 100).reshape(-1, 2)\n",
    "cluster1 = pd.DataFrame(cluster1, columns=[\"x1\", \"x2\"])\n",
    "cluster1[\"y\"] = 0\n",
    "cluster1.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:00.908883Z",
     "start_time": "2025-05-10T03:56:00.902630Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th>x1</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.331587</td>\n",
       "      <td>3.715279</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.454600</td>\n",
       "      <td>2.991616</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.621336</td>\n",
       "      <td>2.279914</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.265512</td>\n",
       "      <td>3.108549</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.004291</td>\n",
       "      <td>2.825400</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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       "</div>"
      ],
      "text/plain": [
       "         x1        x2  y\n",
       "0  4.331587  3.715279  1\n",
       "1  1.454600  2.991616  1\n",
       "2  3.621336  2.279914  1\n",
       "3  3.265512  3.108549  1\n",
       "4  3.004291  2.825400  1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 生成第 2 类模拟数据\n",
    "np.random.seed(10)\n",
    "cluster2 = np.random.normal(3, 1, 100).reshape(-1, 2)\n",
    "cluster2 = pd.DataFrame(cluster2, columns=[\"x1\", \"x2\"])\n",
    "cluster2[\"y\"] = 1\n",
    "cluster2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:01.068392Z",
     "start_time": "2025-05-10T03:56:01.064879Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(100, 3)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 合并两个数据框\n",
    "data = pd.concat([cluster1, cluster2])  # 默认以纵轴 axis=0 方向\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制散点图，更直观展示"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:01.364361Z",
     "start_time": "2025-05-10T03:56:01.218261Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'True Clusters (K=2)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=\"x1\", y=\"x2\", data=cluster1, color=\"k\", label=\"y=0\")\n",
    "sns.scatterplot(x=\"x1\", y=\"x2\", data=cluster2, color=\"b\", label=\"y=1\")\n",
    "plt.legend()\n",
    "\n",
    "plt.title(\"True Clusters (K=2)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "取出数据矩阵 X 和分类变量 y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:01.402334Z",
     "start_time": "2025-05-10T03:56:01.376071Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>KMeans(n_clusters=2, n_init=20, random_state=123)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>KMeans</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.cluster.KMeans.html\">?<span>Documentation for KMeans</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>KMeans(n_clusters=2, n_init=20, random_state=123)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "KMeans(n_clusters=2, n_init=20, random_state=123)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = data.iloc[:, :-1]\n",
    "y = data.iloc[:, -1]\n",
    "\n",
    "# 使用 sklearn 进行 K 均值聚类分析\n",
    "# n_init 表示进行 20 次随机初始化，选择最优的聚类结果\n",
    "model = KMeans(n_clusters=2, random_state=123, n_init=20)  # 创建一个 KMeans 类的实例\n",
    "# 使用 fit 方法进行估计\n",
    "model.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:01.448768Z",
     "start_time": "2025-05-10T03:56:01.437568Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1\n",
      " 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0\n",
      " 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]\n",
      "[[3.16672098 3.07129467]\n",
      " [0.15504503 0.00842918]]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>49</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted   0   1\n",
       "Actual           \n",
       "0           0  50\n",
       "1          49   1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 通过 model 的 labels_ 属性，可以得到每个样例的聚类归属\n",
    "print(model.labels_)\n",
    "# 通过 model 的 cluster_centers_ 属性，可以得到每个聚类的中心位置\n",
    "print(model.cluster_centers_)\n",
    "\n",
    "# 更直观的，通过混淆矩阵进行观察（严格说，这不是真正的混淆矩阵，因为这不是监督学习，只是模拟的正确标签）\n",
    "pd.crosstab(y, model.labels_, rownames=[\"Actual\"], colnames=[\"Predicted\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "通过混淆矩阵可以观察到只有 1 个观测值被错误分类。\n",
    "\n",
    "将分类结果画散点图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:01.704099Z",
     "start_time": "2025-05-10T03:56:01.562410Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated Clusters (K=2)')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=\"x1\", y=\"x2\", data=data[model.labels_ == 0], color=\"k\", label=\"y=0\")\n",
    "sns.scatterplot(x=\"x1\", y=\"x2\", data=data[model.labels_ == 1], color=\"b\", label=\"y=1\")\n",
    "plt.legend()\n",
    "plt.title(\"Estimated Clusters (K=2)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出被错误分类的样本位于两类数据的交叠位置。\n",
    "\n",
    "下面，假设聚类数目为 3，再次进行 K 均值聚类分析："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:01.771087Z",
     "start_time": "2025-05-10T03:56:01.757190Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2,\n",
       "       0, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2,\n",
       "       2, 2, 0, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], dtype=int32)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = KMeans(n_clusters=3, random_state=2, n_init=20)\n",
    "model.fit(X)\n",
    "\n",
    "model.labels_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘制聚类散点图："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.058655Z",
     "start_time": "2025-05-10T03:56:01.896907Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated Clusters (K=3)')"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(x=\"x1\", y=\"x2\", data=data[model.labels_ == 0], color=\"k\", label=\"y=0\")\n",
    "sns.scatterplot(x=\"x1\", y=\"x2\", data=data[model.labels_ == 1], color=\"b\", label=\"y=1\")\n",
    "sns.scatterplot(\n",
    "    x=\"x1\", y=\"x2\", data=data[model.labels_ == 2], color=\"cornflowerblue\", label=\"y=2\"\n",
    ")\n",
    "plt.legend()\n",
    "plt.title(\"Estimated Clusters (K=3)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "假设聚类数目为 4，继续分析："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.112942Z",
     "start_time": "2025-05-10T03:56:02.092937Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "103.88964922675225"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = KMeans(n_clusters=4, random_state=4, n_init=1)\n",
    "model.fit(X)\n",
    "model.inertia_  # 组内平方总和"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.216913Z",
     "start_time": "2025-05-10T03:56:02.163789Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "103.85410947586236"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = KMeans(n_clusters=4, random_state=4, n_init=30)\n",
    "model.fit(X)\n",
    "model.inertia_  # 组内平方总和，相对 1 次初始化值有所降低"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "因此，进行 1 次初始化时的结果是局部最小值，并非全局最小值。\n",
    "\n",
    "当增大 `n_init` 的值时，增加到 1000，SSE 也是相同的，这很可能就是全局最小值。\n",
    "\n",
    "实际上的 K 值是 2 个，实际情况下无法得知最佳的 K。\n",
    "\n",
    "首先，使用手肘法确认最佳的 K 值，使用 `for` 循环计算不同 K 值时的 SSE："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.543434Z",
     "start_time": "2025-05-10T03:56:02.256315Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n",
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[626.7960530195322,\n",
       " 165.69714015317402,\n",
       " 134.29161574012807,\n",
       " 103.87529585375258,\n",
       " 83.67845516333534,\n",
       " 65.15934028247376,\n",
       " 58.11484194148171,\n",
       " 49.41041946425872,\n",
       " 44.09452611114926,\n",
       " 39.91760823154711,\n",
       " 35.380323608196974,\n",
       " 31.76697915698022,\n",
       " 28.824622502934943,\n",
       " 26.08880187882634,\n",
       " 22.518962385041853]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sse = []\n",
    "for k in range(1, 16):\n",
    "    model = KMeans(n_clusters=k, random_state=1, n_init=20)\n",
    "    model.fit(X)\n",
    "    sse.append(model.inertia_)\n",
    "sse"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绘图更直观的展示 SSE："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.662823Z",
     "start_time": "2025-05-10T03:56:02.570018Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'K-means Clustering')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, 16), sse, \"o-\")\n",
    "plt.axhline(sse[1], color=\"k\", linestyle=\"--\", linewidth=1)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"SSE\")\n",
    "plt.title(\"K-means Clustering\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在 K=2 时拐弯，因此应该选择 K=2 时聚类。\n",
    "\n",
    "下面使用 AIC 信息准则选择聚类数目 K，信息准则的公式为：\n",
    "\n",
    "$$\n",
    "AIC(K) = SSE(K) + 2pK\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.682558Z",
     "start_time": "2025-05-10T03:56:02.678559Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([630.79605302, 173.69714015, 146.29161574, 119.87529585,\n",
       "       103.67845516,  89.15934028,  86.11484194,  81.41041946,\n",
       "        80.09452611,  79.91760823,  79.38032361,  79.76697916,\n",
       "        80.8246225 ,  82.08880188,  82.51896239])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aic = sse + 2 * 2 * np.arange(1, 16)\n",
    "aic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.743401Z",
     "start_time": "2025-05-10T03:56:02.739937Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(79.38032360819697)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(aic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.799486Z",
     "start_time": "2025-05-10T03:56:02.796266Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(10)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(aic)  # 获取最小值的索引"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "画图展示聚类数目和 AIC 的关系："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.957619Z",
     "start_time": "2025-05-10T03:56:02.858954Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'K-means Clustering')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.plot(x轴数据, y轴数据, color颜色, linestyle线条样式, linewidth线条宽度, marker标记样式, markersize标记大小, label标签)\n",
    "plt.plot(range(1, 16), aic, \"o-\")\n",
    "# 画垂直线\n",
    "# plt.axvline(x轴上的第几个位置<从1开始>, color颜色, linestyle线条样式, linewidth线条宽度)\n",
    "plt.axvline(np.argmin(aic) + 1, color=\"k\", linestyle=\"--\", linewidth=1)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"AIC\")\n",
    "plt.title(\"K-means Clustering\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "显然，聚类数目太多，导致过拟合，这是因为 AIC 惩罚不够严厉，下面使用 BIC 信息准则，并展示结果。\n",
    "\n",
    "BIC 信息准则公式：\n",
    "\n",
    "$$\n",
    "BIC(K) = SSE(K) + \\text{ln(n)}\\cdot pK\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:02.973923Z",
     "start_time": "2025-05-10T03:56:02.971241Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([636.00639339, 184.1178209 , 161.92263686, 140.71665734,\n",
       "       129.73015702, 120.42138251, 122.58722455, 123.09314244,\n",
       "       126.98758946, 132.02101195, 136.6940677 , 142.29106362,\n",
       "       148.55904734, 155.03356709, 160.67406796])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bic = sse + np.log(100) * 2 * np.arange(1, 16)\n",
    "bic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:03.039866Z",
     "start_time": "2025-05-10T03:56:03.036975Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(120.42138251433087)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(bic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:03.102475Z",
     "start_time": "2025-05-10T03:56:03.099804Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.int64(5)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.argmin(bic)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:03.248810Z",
     "start_time": "2025-05-10T03:56:03.158231Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'K-means Clustering')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(1, 16), bic, \"o-\")\n",
    "plt.axvline(np.argmin(bic) + 1, color=\"k\", linestyle=\"--\", linewidth=1)\n",
    "plt.xlabel(\"K\")\n",
    "plt.ylabel(\"BIC\")\n",
    "plt.title(\"K-means Clustering\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看到，选择了 K=6 作为聚类数目，仍然不可靠，可以看出，使用传统的选择 K 的数目的方法并不可靠。\n",
    "\n",
    "下面使用真实的 iris 数据集进行 K 均值聚类操作。\n",
    "\n",
    "为了在 3 维空间内可视化，仅使用前 3 个特征进行处理（花萼长度、花萼宽度和花瓣长度）。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:56:05.655728Z",
     "start_time": "2025-05-10T03:56:03.265367Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  sepal_width  petal_length  petal_width species\n",
       "0           5.1          3.5           1.4          0.2  setosa\n",
       "1           4.9          3.0           1.4          0.2  setosa\n",
       "2           4.7          3.2           1.3          0.2  setosa\n",
       "3           4.6          3.1           1.5          0.2  setosa\n",
       "4           5.0          3.6           1.4          0.2  setosa"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 从 seaborn 中导入 iris 数据集\n",
    "iris = sns.load_dataset(\"iris\")\n",
    "iris.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将特征编码"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T03:58:15.473473Z",
     "start_time": "2025-05-10T03:58:15.470692Z"
    }
   },
   "outputs": [],
   "source": [
    "Dict = {\"setosa\": 0, \"versicolor\": 1, \"virginica\": 2}  # 将映射定义为字典\n",
    "iris.species = iris.species.map(Dict)  # 使用 map() 方法完成转换"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "画前三个特征的散点图，并根据鸢尾花种类上色："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T04:19:25.798465Z",
     "start_time": "2025-05-10T04:19:25.675956Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'petal_length')"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(10, 8))\n",
    "# add_subplot() 方法添加子图\n",
    "# 111 表示 1 行 1 列 1 个子图，projection 只能在创建子图时指定\n",
    "# projection=\"3d\" 表示创建 3D 子图\n",
    "ax = fig.add_subplot(111, projection=\"3d\")\n",
    "ax.scatter(\n",
    "    iris[\"sepal_length\"],\n",
    "    iris[\"sepal_width\"],\n",
    "    iris[\"petal_length\"],\n",
    "    c=iris[\"species\"],\n",
    "    cmap=\"rainbow\",\n",
    ")\n",
    "ax.set_xlabel(\"sepal_length\")\n",
    "ax.set_ylabel(\"sepal_width\")\n",
    "ax.set_zlabel(\"petal_length\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以看出，3 类不同的鸢尾花聚集在不同的区域，可以使用 K 均值聚类进行聚类。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T05:20:33.531892Z",
     "start_time": "2025-05-10T05:20:33.516156Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "d:\\Code\\AI\\Machine_Learning\\machine-learning\\.ml-venv\\Lib\\site-packages\\sklearn\\cluster\\_kmeans.py:1419: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2,\n",
       "       2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0], dtype=int32)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X3 = iris.iloc[:, :3]\n",
    "model = KMeans(n_clusters=3, random_state=1, n_init=20)\n",
    "model.fit(X3)\n",
    "model.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T05:31:21.188261Z",
     "start_time": "2025-05-10T05:31:21.185156Z"
    }
   },
   "outputs": [],
   "source": [
    "# 转换为数据框\n",
    "labels = pd.DataFrame(model.labels_, columns=[\"label\"])\n",
    "d = {0: 1, 1: 0, 2: 2}\n",
    "pred = labels.label.map(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T05:31:41.679156Z",
     "start_time": "2025-05-10T05:31:41.671270Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>50</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>45</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>13</td>\n",
       "      <td>37</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted   0   1   2\n",
       "Actual               \n",
       "0          50   0   0\n",
       "1           0  45   5\n",
       "2           0  13  37"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 展示混淆矩阵\n",
    "table = pd.crosstab(iris.species, pred, rownames=[\"Actual\"], colnames=[\"Predicted\"])\n",
    "table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-05-10T05:32:04.307988Z",
     "start_time": "2025-05-10T05:32:04.305237Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.88)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accuracy = np.trace(table) / len(iris)\n",
    "accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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